UNIT H1 Angles and Symmetry Activities

Transcription

1 UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)

2 ACTIVITY H1.1 Mathematics SKE, Strand H Lines of Symmetry Each of the 3 3 squares below has 3 shaded squares and one line of symmetry. 1. How many more ways can you find to shade 3 squares in a 3 3 square so that there is only one line of symmetry? Record your patterns. 2. (a) In a 3 3 square find a pattern of 3 shaded squares which has 2 lines of symmetry. (b) Is it the only one? If not, try to find all such patterns. 3. Using a 3 3 square, find all the possible patterns of 4 shaded squares which have (a) one line of symmetry (b) two lines of symmetry (c) three lines of symmetry (d) four lines of symmetry. Extension Do a similar study for a 4 4 square with different patterns of (a) 3 shaded squares (b) 4 shaded squares (c) 5 shaded squares (d) 6 shaded squares.

3 ACTIVITY H1.2 Rotational and Line Symmetry 1. For each polygon below: (a) (b) (c) use dotted lines to show the lines of symmetry, if any; check whether it has rotational symmetry and if so, state its order; mark the centre of rotational symmetry with a cross (x). (i) (ii) (iii) (iv) Order Order Order Order (v) (vi) (vii) (viii) Order Order Order Order 2. Use the results from Question 1 to complete the following table. Name of Number of Lines Order of Rotational Polygon of Symmetry Symmetry (i) Isosceles triangle (ii) Equilateral triangle (iii) Rectangle (iv) Square (v) Parallelogram (vi) Rhombus (vii) (viii) Kite Trapezium

4 ACTIVITY H1.3 Symmetry of Regular Polygons 1. For each of the following regular polygons, draw in the lines of symmetry and locate the centre of rotational symmetry. 2. Use your answers to question 1 to complete the following table. Name of Number Number of Lines Order of Rotational Polygon of sides of Symmetry Symmetry Hexagon Octagon Nonagon Decagon 3. Use the completed table in question 2 to find: (a) (b) the number of lines of symmetry, the order of rotational symmetry, for (i) (ii) a regular decagon, a regular twenty-sided polygon, (iii) a regular n-gon.

5 ACTIVITY H1.4 Mathematics SKE, Strand H Interior Angles in Polygons You can find the sum of the interior angles in any polygon by dividing it up into triangles with lines connecting the vertices. For example, the hexagon shown opposite has been divided into 4 internal triangles. The sum of all the interior angles of the hexagon is equal to the sum of all the angles in each triangle; so sum of interior angles = = Repeat the same analysis for the following shapes: (a) quadrilateral (b) pentagon (c) heptagon (d) octagon (e) nonagon (f) decagon. 2. Copy and complete the table. Name of Number Number of Sum of Polygon of sides Triangles Interior Angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Extension What is the formula for the sum of the interior angles of a polygon with n sides?

6 ACTIVITIES H1.1 H.4 Notes and Solutions Notes and solutions are given only where appropriate. H possibilities or, or 3. (a) 4 basic designs (b) none (c) none (d) or H Polygon No. of lines of symmetry Order of rotational symmetry Isosceles 1 1 Equilateral 3 3 Rectangle 2 2 Square 4 4 Parallelogram 0 2 Rhombus 2 2 Kite 1 1 Trapezium 0 1 H Polygon No. of sides No. of lines Order of rotational of symmetry symmetry Hexagon Octagon Nonagon Decagon H1.4 For a polygon with n sides, the sum of the interior angles is 180( n 2) ; hence the values in the table should be 180, 360, 540, 720, 900, 1080, 1160, 1340.